Design of economical fuzzy systems using least fuzzy rules

Fuzzy systems are proved to be universal approximators, yet they may need a large number of fuzzy rules for high approximation accuracy. For this rule-explosion problem, we introduce the idea on design of economical fuzzy systems. Given a specified architecture, a fuzzy system is called economical if it uses least fuzzy rules and at the same time it approximates the given function at a pre-required approximation accuracy. The essence of our solution is to partition the domain of the function nonuniformly. We investigate the approximation formulations of two commonly used fuzzy systems: the Mamdani and the TSK fuzzy systems with linear consequent. Then the economical fuzzy system design problem is formulated mathematically. Finally, an approximate algorithms is proposed toward designing Mamdani type economical fuzzy systems